Extreme Multistability in a Hamiltonian-Driven System

In this paper, we present a study of a system of unidirectionally coupled maps that approximates a billiard with oscillating boundaries. The system consists of a dissipative 2D map affected by a conservative 2D map describing chaotic billiards with fixed boundaries. In this paper, we show the coexistence of regular and strange attractors, which we detect using spectral and Lyapunov analyses. It seems that for every small variation in driving the dissipative system by the conservative system, separate attractors appear. Furthermore, we show that orbits with slightly different initial conditions lead to different separated attractors, suggesting that an infinite set of attractors exists in the system.